Deep neural networks (DNNs) can automatically fetch specific features from seismic data, which can be used in the process of multiple elimination. An extended single-sided autofocusing guided by an inverse-scattering theory is introduced to remove internal multiples in a data-driven manner, which can be used as labels in DNNs. In this research, we have developed a novel workflow to explore the potential of neural networks in identifying the internal multiples with the guidance of inverse-scattering theory. In particular, we use the U-net with a self-attention (SA) block during the training process, which could extract features from seismic data effectively. The neural network is fed with training data pairs, consisting of the shot records with internal multiples, and the primary-only datasets as labels, which are generated by an extended single-sided autofocusing method. The testing pairs show that internal multiple elimination via the neural network takes the advantage of the extended single-sided autofocusing method and is cheaper when the neural network is well-trained. The numerical results demonstrate the promising performances of the SA U-net method in terms of noise resistance, internal multiples elimination, and the reverse time migration (RTM) images, in comparison with the extended single-sided autofocusing method.

Full waveform inversion (FWI) is, as an optimization problem, strongly nonconvex and is influenced intensely by the cycle skipping issue, especially for multiparameter inversions like the elastic case. When there are strong scattering heterogeneities in the target media, there will be more challenges for the inversion problem. The direct envelope inversion strategy uses the envelope Fréchet derivative to tackle the cycle skipping problem for strong scattering inversion and has been effectively used for the acoustic case. We extend the direct envelope inversion method to the elastic situation in this letter. We derive the elastic envelope Fréchet derivative and show how the strong scattering multiparameter elastic inversion is accomplished under the direct envelope inversion framework. Numerical tests with the SEG/EAGE salt velocity model proved the effectiveness of this method for the strong scattering elastic medium.

Marchenko equation-based imaging methods have been proved as an effective way to remove the internal multiples. Conventional Marchenko imaging needs the reflection response at the surface and an estimate of the direct arrival times from the virtual source point to the acquisition surface. It contains the procedure of redatuming and imaging. The redatuming process is valid only for layered media with a moderately curved interface. We rederive the single reflection retrieval by a focusing source method based on the scattering theory and avoid the use of redatuming plane and the upgoing/downgoing decomposition. This scheme reproduces a new data free from internal multiples for complex structures, such as salt dome. Our theory/method expands the application range of Marchenko imaging and internal multiple elimination. With an artifact-free image obtained by this procedure, an illumination compensation can be further applied to obtain a high-fidelity image, especially in the subsalt area. Numerical examples using the 2-D SEG/EAGE salt model are shown to validate this method.

Least-squares reverse time migration (LSRTM) attempts to produce a high-quality image for complicated subsurface structures. However, large amplitude discrepancies between the synthetic and observed seismic data are problematic for high-resolution imaging. Alternatively, correlative LSRTM (CLSRTM) misfit has been proposed to improve the imaging quality of complicated structures. However, the CLSRTM ignores the local characteristics of the 2-D seismic data. Thus, we developed a 2-D local correlative misfit for LSRTM (2-D-LCLSRTM) to improve the imaging resolution. In this case, a 2-D sliding window was used to obtain local-scale seismic data. A 2-D correlation method was then used to measure the similarity between the local-scale synthetic and observed data. Consequently, the 2-D-LCLSRTM misfit could reduce amplitude constraints and emphasize phase similarity, which has a potential for improving deep structure as it can boost weak seismic signals. To suppress the migration artifacts, we incorporated the sparsity promotion method with the 2-D-LCLSRTM misfit and used the fast iterative shrinkage-thresholding algorithm (FISTA) to solve it iteratively. In the numerical examples, a Marmousi model, a Salt model, and a marine field seismic dataset were used to test the effectiveness of the 2-D-LCLSRTM method. Compared with the commonly used RTM and sparsity promotion-based CLSRTM methods, the 2-D-LCLSRTM with sparsity promotion can better image deep reflectors and obtain high-resolution imaging results.

The exploration capacity of full waveform inversion (FWI) for deep targets is affected by the acquisition geometry, complexity of overlying strata and dip angle of the target, etc. It is of great importance to analyze the relationship between the dip angle of the target reflector and the incident/scattered angle of the wavefields near the target, so as to achieve the illumination distribution and improve the inversion quality accordingly. We propose an angle domain illumination compensated FWI strategy, which utilizes the local resolution function as preconditioning to the gradient of FWI in the local angle domain, in order to improve the inversion capability for deep targets. The local resolution function describes the inversion capacity for the local target in the target dip coordinate, which can be generated from the local illumination matrix that contains the illumination information for the target from different incident and scattering directions. The Marmousi model and the SEG/EAGE salt model are used to show the validity of this method. Results from the numerical experiments prove that the proposed method can effectively improve the inversion performance as well as increase the convergence of FWI.

Q-compensated reverse-time migration ( Q-RTM) has been proven as an efficient method for seismic imaging with high fidelity. However, the source (forward) and receiver (backward) wavefields propagate along the opposite direction of time, and the recursive computation with the out-of-order access requires that all the wavefields of source propagation should be stored on the hard disk. For massive amounts of seismic data, saving the source wavefield from the central processing unit (CPU) [or graphics processing unit (GPU)] device to the disk and loading these data from the hard disk to the CPU (or GPU) device become extremely intensive in time and storage, which has been a bottleneck of Q-RTM. Several methods have been developed to reduce the huge wavefield storage in acoustic media, but are not applicable in the attenuated media. In this letter, we present a reversible hybrid absorbing boundary condition for Q-RTM, which is implemented by mixing the reversible attenuation and the random boundary conditions. Based on our developed new boundary, we just need to save the wavefield at the last one or two time steps in the forward process and then reconstruct the source wavefield in the time-reversal order. Numerical results demonstrate that the method can avoid the huge seismic data input and output (I/O) requirement and improve the computational efficiency dramatically.

A new Gaussian beam (GB) Born modeling method is presented in this letter to simulate the wavefields of single scattering events in visco-acoustic media. This approach allows the accurate computation of synthetic seismograms or waveforms for the visco-acoustic media. Our method relies on the GB summation method, in which the attenuation effects are taken into account by incorporating a frequency-dependent dissipation function into beam calculation. The key to efficiency is that the Born modeling kernel is evaluated in the time domain based on the filter-bank technique. The proposed method is tested with both 2-D and 3-D numerical examples and the results demonstrate its capability to simulate wavefields in complex structures, as well as its marked advantage in efficiency over finite-difference wave equation modeling.

Full waveform inversion (FWI) is a powerful tool to understand the real complicated earth model. As FWI is a highly nonlinear problem and depends strongly on the initial model, how to effectively retrieve the large-scale background model is critical for the success of FWI. For elastic FWI (EFWI), the inversion challenge increases because the P-wave and S-wave are coupled together if no mode separation technologies are applied. In this article, we develop a new EFWI strategy, where we simultaneously implement the angle decomposition and mode separation for the wavefield. Based on the analysis of radiation patterns of different parameters and the fact that small scattering angles correspond to large-scale model perturbations, we can retrieve the large-scale background model of the P-wave velocity with pure small scattering angle P-P mode wavefield. On the other hand, the pure small scattering angle S-S, S-P, and P-S mode wavefields are used to estimate the large-scale background model of the S-wave velocity. The correctly retrieved large-scale background models further guarantee the success of subsequent fine structure retrieving for the P- and S-wave velocity models by using different wave modes. The proposed method is able to reduce the cycle-skipping problem and the multiparameter crosstalk problem simultaneously. Numerical examples show that the proposed method provides much improved inversion results than the conventional EFWI, which demonstrates the validity of the proposed method.

Strong scattering perturbations like large-scale salt structures in the model parameters make the task of full-waveform inversion more difficult than the weak scattering inversion. The problem becomes even tougher when both the velocity and density are taken into consideration because the tradeoff among the multiparameters further influences the inversion. In order to accomplish effective estimation for both the velocity and density with strong scatterings, we introduce an angle domain direct envelope inversion method with the new Fréchet derivative. The direct envelope inversion method works well on salt structure recovery for the velocity model. However, it may not work well if the density parameter is considered. By introducing angle information into the inversion, the tradeoff between velocity and density can be greatly reduced. Numerical examples using the SEG/EAGE salt model show that by accomplishing the direct envelope inversion in the angle domain, both the velocity and density estimation with strong scattering perturbations are greatly improved, which demonstrates the validity of the proposed method.

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.

Time-frequency analysis can reveal local variations and allow for separation of phase and amplitude information of nonstationary seismic waveforms. Seismic signals are used since long as a robust tool for inversion of underground structures, as has been the practice in geophysical exploration. However, the mixing of phase and amplitude in seismic data increases the nonlinearity of seismic inversion. The authors first use Gabor transform to separate the phase and amplitude information of envelope data, and then introduce an adaptive factor into the misfit function to redistribute the weight of phase and amplitude information for direct envelope inversion (DEI) in the time-frequency domain. By adopting this procedure, greater flexibility can be achieved in operating the local phase of envelope and waveform spectra to enhance stability of multiscale phase inversion. For DEI, the direct envelope Fréchet derivative is used, and thus, no weak scattering assumption is imposed on the joint multiscale DEI of phase and amplitude (PADEI). Compared with the DEI method, the PADEI can better recover the deeper parts of salt-bottom and subsalt structures by boosting the signal energy and weakening the nonlinearity of the waveform inversion.

Simultaneous-source acquisition, breaking the limit of conventional seismic acquisition, is a rapidly evolving research field, due to its advantage in reducing survey time and improving data quality. The benefits of simultaneous-source acquisition are compromised by the intense blending interference. Separating a blended record into a group of individual records, known as “deblending” is one of the most popular solution to the problem. However, the blended records are often corrupted by random noise, which causes difficulties in separation. In an iterative deblending algorithm, the incoherent interference can be simulated and subtracted from the blended record. When the random noise is strong, it is difficult to simulate the incoherent interference. In this paper, we propose a hybrid-sparsity constraint model that applies the dictionary learning into the deblending framework that is based on the sparsity-promoting transform to deal with extremely noisy simultaneous source data. The dictionary learning with fine-tuned adaptation can learn the incoherent interference into atoms and reject random noise. Then, the sparse transform-based framework is implemented to iteratively separate the signal and interference. We use two synthetic examples to demonstrate the advantage of the proposed method in extremely noisy situations. Two field examples further confirm the superior deblending performance of the proposed method for the noisy simultaneous-source data over the curvelet transform-based and rank reduction-based methods.

The dreamlet (drumbeat-beamlet) transform can provide us an efficient method to represent physical wavefield, because the dreamlet basis satisfies automatically the wave equation, which is a distinctive feature different from mathematical basis, such as Fourier and curvelet. It can obtain an estimation of true signal from the observed noisy data by abandoning those insignificant components in the dreamlet domain. However, we have found that a more accurate estimation can be achieved by a damped version of the dreamlet representation. We have theoretically derived the damped dreamlet representation and given its geometric interpretation and analysis. Two applications of the proposed method have been explored in this paper: seismic random noise suppression and seismic data interpolation. Various examples demonstrate that the damped dreamlet representation-based technique has a superior performance compared with the mathematical-basis-based representation and rank-reduction-based techniques.